Macroeconomic and financial time series are often tested for the presence of non linearity effects. Sometimes, small patches of extremal observations may wrongly influence non linearity tests. In this paper a robust analysis of the Lagrange Multiplier (LM) test for GARCH components is suggested. With Monte Carlo simulation we show that extreme observations might cause over-estimation of the number of GARCH components, with the main contribution consisting by introducing the forward search method into the GARCH model family. Using robust estimators of regression coefficients and graphical displays of results, the effect of influential observations on estimates can be efficiently monitored. Analyzing macroeconomic and financial time series we show that identifying the order of a GARCH model can be unduly influenced by a few isolated large values, and extremal observations affect p−values and t−statistics in an unexpected manner.